A control mechanism of the above mentioned kind has been disclosed in DE-OS 31 30 871. Pressurized fluid is optionally fed from the main pressure system of the control mechanism via regulating valves to the actuation spaces of the lock-up clutch so that the lock-up clutch is in an engaged, disengaged, or slipping condition. Attached to a return flow of one of the regulating valves which is optionally connectable with one of the two actuation spaces is the lubricant line which leads via the oil cooler to the lubrication system of the transmission. In the initial phase, when the lock-up clutch is engaged, only a small amount of lubricant from the actuation space serving for disengaging reaches the lubrication points of the transmission via the radiator. A complete collapse of the lubricant pressure, which can result in damage to the transmission, occurs when the control valve of the regulating valve is in its central position so that lubricant cannot reach the lubrication points via the radiator either from the interior of the converter or from the main pressure line.